TDD (time division duplexing) is known as one type of mobile communication scheme. Since frequency bands for an uplink and those for a downlink are the same in TDD, channel states on the air are basically the same between the uplink and the downlink. That the channel states are the same in the uplink and in the downlink is called “channel reciprocity.”
Due to such channel reciprocity, theoretically, a radio base station is able to estimate downlink channel states based on uplink channel state information and determine parameters for downlink transmission. Determining parameters for downlink transmission based on uplink channel state information is advantageous as compared to determining parameters for downlink transmission based on downlink channel state information measured by a mobile station (user equipment) because the downlink channel state information need not be reported from the mobile station to the radio base station.
However, in reality, due to variations in characteristics of transmitting circuits and variations in characteristics of receiving circuits, downlink channel state information measured by a mobile station in a TDD mobile communication system is different from uplink channel state information measured by a radio base station. These characteristics change depending on the environment, such as the temperature and humidity, and differ among antennas in the same device. Hereafter, such characteristics of transmitting circuit are called “transmitting gain” and characteristics of receiving circuit are called “receiving gain.”
For this reason, calibration of channel coefficients is proposed when parameters for downlink transmission is determined based on uplink channel coefficients (e.g., Non-Patent Documents 1 and 2). Such calibration of channel coefficients in a TDD mobile communication system is called radio frequency calibration (RF calibration) or antenna calibration.
Antenna calibration described in Non-Patent Document 1 will be described with reference to FIG. 1. As shown in FIG. 1, a radio base station 10 includes N number of transceiving antenna elements 111 to 11N, and a user equipment 100 includes M number of transceiving antenna elements 1011 to 101M. Due to channel reciprocity between the uplink and the downlink, the following equation (1) can be obtained.gm,n(UL)=gm,n(DL)  (1)
Here, gm,n(UL) an uplink channel gain on the air from an antenna element 101m of the user equipment 100 to an antenna element 11n of the radio base station 10, and gm,n(DL) is a downlink channel gain on the air from an antenna element 11n of the radio base station 10 to an antenna element 101m of the user equipment 100. The subscript m is a number for an antenna in the user equipment 100, and the subscript n is a number for an antenna in the radio base station 10.
The radio base station 10, with respect to antenna elements 111 to 11N, has transmitting gains TeNB,1 to TeNB,N, respectively, for downlink transmission and has receiving gains ReNB,1 ReNB,N, respectively, for uplink reception. The user equipment 100, with respect to antenna elements 1011 to 101M, has receiving gains RUE to RUE,M, respectively, for downlink reception and has transmitting gains TUE,1 to TUE,M, respectively, for uplink transmission.
Accordingly, an uplink channel coefficient hm,n(UL) measured in the radio base station 10 can be expressed with the following equation (2).hm,nUL=TUE,m·gm,n(UL)·ReNB,n  (2)A downlink channel coefficient hm,n(DL) measured in the user equipment 100 can be expressed with the following equation (3).hm,n(DL)=TeNB,n·gm,n(DL)·RUE,m  (3)
As a result of TUE,m·ReNB,n≠TeNB,nRUE,m, hm,n(UL)≠hm,n(DL) can be obtained.
Therefore, when the radio base station 10 determines parameters for downlink transmission (e.g., downlink transmitting precoding matrix) based on uplink channel states alone, the determined parameters may not be appropriate for the reception in the user equipment 100. In view of this, the user equipment 100 applies calibration coefficients cUE,m to uplink signals transmitted with respective antennas, and the radio base station 10 applies calibration coefficients ceNB,n to downlink signals transmitted with respective antennas.
The calibrated uplink channel coefficient am,n(UL) is expressed as follows.am,n(UL)=cUE,m·hm,n(UL)  (4)The calibrated downlink channel coefficient am,n(DL) is expressed as follows.am,n(DL)ceNB,n·hm,n(DL)  (5)
In order to calibrate channel reciprocity distorted by the transmitting gain and the receiving gain, the calibrated channel coefficient should satisfy the following equation.
                                                        a                              1                ,                1                                            (                UL                )                                                    a                              1                ,                1                                            (                DL                )                                              =                                                                      a                                      m                    ,                    n                                                        (                    UL                    )                                                                    a                                      m                    ,                    n                                                        (                    DL                    )                                                              ⁢                                                          ⁢              m                        =            1                          ,        …        ⁢                                  ,                              M            ⁢                                                  ⁢            n                    =          1                ,        …        ⁢                                  ,        N                            (        6        )            
Antenna calibration described in Non-Patent Document 1 is carried out by appropriate determination of calibration coefficients cUE,m and ceNB,n such that the following equations (7) and (8), which can be derived from equations (2), (3), and (6), are satisfied.
                                                        c                              UE                ,                1                                      ·                          T                              UE                ,                1                                                          R                          UE              ,              1                                      =                                                            c                                  UE                  ,                  2                                            ·                              T                                  UE                  ,                  2                                                                    R                              UE                ,                2                                              =                                          ⁢                      …            ⁢                                                  =                                                            c                                      UE                    ,                    M                                                  ·                                  T                                      UE                    ,                    M                                                                              R                                  UE                  ,                  M                                                                                        (        7        )                                                                    c                              eNB                ,                1                                      ·                          T                              eNB                ,                1                                                          R                          eNB              ,              1                                      =                                                            c                                  eNB                  ,                  2                                            ·                              T                                  eNB                  ,                  2                                                                    R                              eNB                ,                2                                              =                                          ⁢                      …            ⁢                                                  =                                                            c                                      eNB                    ,                    N                                                  ·                                  T                                      eNB                    ,                    N                                                                              R                                  eNB                  ,                  N                                                                                        (        8        )            
Next, a more specific antenna calibration method that can be derived from the antenna calibration method described in Non-Patent Document 1 will be described. From equations (1), (2), and (3), when antenna calibration is not carried out, the relationship between the uplink channel coefficient and the downlink channel coefficient can be expressed by the following equation (9).
                              h                      m            ,            n                                (            DL            )                          =                                            R                              UE                ,                m                                                    T                              UE                ,                m                                              ⁢                                          ⁢                      h                          m              ,              n                                      (              UL              )                                ⁢                                    T                              eNB                ,                n                                                    R                              eNB                ,                n                                                                        (        9        )            
When equation (9) is expressed in a matrix format, equation (10) can be obtained. In other words, when antenna calibration is not carried out, the relationship between the uplink channel matrix and the downlink channel matrix can be expressed by equation (10).
                              H          DL                =                              [                                                                                v                    1                                                                                                                                                                                                                                                    0                                                                                                                                                                                          v                    2                                                                                                                                                                                                                                                                                                                                                                                                                                                                ⋱                                                                                                                                                                      0                                                                                                                                                                                                                                                      v                    M                                                                        ]                    ⁢                                    H              UL                        ⁡                          [                                                                                          w                      1                                                                                                                                                                                                                                                                                0                                                                                                                                                                                                                w                      2                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ⋱                                                                                                                                                                                          0                                                                                                                                                                                                                                                                                  w                      M                                                                                  ]                                                          (        10        )            Here, HDL is a downlink channel matrix and can be expressed as follows.
      H    DL    =      [                                        h                          m              ,              n                                      (              DL              )                                                            h                          m              ,              n                                      (              DL              )                                                …                                      h                          m              ,              n                                      (              DL              )                                                                        h                          m              ,              n                                      (              DL              )                                                            h                          m              ,              n                                      (              DL              )                                                …                                      h                          m              ,              n                                      (              DL              )                                                            ⋮                                                                                                                          ⋮                                                  h                          m              ,              n                                      (              DL              )                                                            h                          m              ,              n                                      (              DL              )                                                …                                      h                          m              ,              n                                      (              DL              )                                            ]  
HUL is an uplink channel matrix and can be expressed as follows.
      H    UL    =      [                                        h                          m              ,              n                                      (              UL              )                                                            h                          m              ,              n                                      (              UL              )                                                …                                      h                          m              ,              n                                      (              UL              )                                                                        h                          m              ,              n                                      (              UL              )                                                            h                          m              ,              n                                      (              UL              )                                                …                                      h                          m              ,              n                                      (              UL              )                                                            ⋮                                                                                                                          ⋮                                                  h                          m              ,              n                                      (              UL              )                                                            h                          m              ,              n                                      (              UL              )                                                …                                      h                          m              ,              n                                      (              UL              )                                            ]  
Thus, equation (10) can be rewritten as in the following equation (11).
                              H          DL                =                                            [                                                                                          v                      1                                                                                                                                                                                                                                                                                0                                                                                                                                                                                                                v                      2                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ⋱                                                                                                                                                                                          0                                                                                                                                                                                                                                                                                  v                      M                                                                                  ]                        ⁡                          [                                                                                          h                                              m                        ,                        n                                                                    (                        UL                        )                                                                                                                        h                                              m                        ,                        n                                                                    (                        UL                        )                                                                                                  …                                                                              h                                              m                        ,                        n                                                                    (                        UL                        )                                                                                                                                                        h                                              m                        ,                        n                                                                    (                        UL                        )                                                                                                                        h                                              m                        ,                        n                                                                    (                        UL                        )                                                                                                  …                                                                              h                                              m                        ,                        n                                                                    (                        UL                        )                                                                                                                                  ⋮                                                                                                                                                                                                                                                            ⋮                                                                                                              h                                              m                        ,                        n                                                                    (                        UL                        )                                                                                                                        h                                              m                        ,                        n                                                                    (                        UL                        )                                                                                                  …                                                                              h                                              m                        ,                        n                                                                    (                        UL                        )                                                                                                        ]                                ⁢                                                 [                                                                                          w                      1                                                                                                                                                                                                                                                                                0                                                                                                                                                                                                                w                      2                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ⋱                                                                                                                                                                                          0                                                                                                                                                                                                                                                                                  w                      M                                                                                  ]                                                          (        11        )            
wn in equations (10) and (11) is a parameter for the radio base station 10 and is expressed by wn=TeNB,n/ReNB,n, and vn is a parameter for the user equipment 100 and is expressed by vm=RUE,m/TUE,m.
When antenna calibration described in Non-Patent Document 1 is carried out, equations (7) and (8) are satisfied. Equation (8) can be rewritten as equation (12), and equation (7) can be rewritten as equation (13).α1=α2= . . . =αM  (12)β1=β2= . . . =βN  (13)
Here, αn is a parameter for the radio base station 10 that has been calibrated with a calibration coefficient ceNB,n, and βm is a parameter for the user equipment 100 that has been calibrated with a calibration coefficient cUE,m·αn and βm are expressed as follows.
                                          α            n                    =                    ⁢                                                    c                                  eNB                  ,                  n                                            ·                              T                                  eNB                  ,                  n                                                                    R                              eNB                ,                n                                                                                  =                    ⁢                                    c                              eNB                ,                n                                      ·                          w              n                                                                                    β            n                    =                    ⁢                                                    c                                  UE                  ,                  m                                            ·                              T                                  UE                  ,                  m                                                                    R                              UE                ,                m                                                                                  =                    ⁢                                    c                              UE                ,                m                                      ·                          v              m                                          
When such antenna calibration is carried out, the relationship between the uplink channel matrix and the downlink channel matrix can be expressed by the following equation (14).
                              H          DL                =                              [                                                                                β                    1                                                                                                                                                                                                                                                    0                                                                                                                                                                                          β                    2                                                                                                                                                                                                                                                                                                                                                                                                                                                                ⋱                                                                                                                                                                      0                                                                                                                                                                                                                                                      β                    M                                                                        ]                    ⁢                                    H              UL                        ⁡                          [                                                                                          α                      1                                                                                                                                                                                                                                                                                0                                                                                                                                                                                                                α                      2                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ⋱                                                                                                                                                                                          0                                                                                                                                                                                                                                                                                  α                      N                                                                                  ]                                                          (        14        )            
Equation (14) can be rewritten as equation (15) from equations (12) and (13).
                                                                        H                DL                            =                            ⁢                                                                    α                    1                                    ·                                      β                    1                                                  ⁢                I                ⁢                                                                  ⁢                                  H                  UL                                ⁢                                                                  ⁢                I                                                                                        =                            ⁢                                                                    α                    1                                    ·                                      β                    1                                                  ⁢                                  H                  UL                                                                                        (        15        )            
It can be understood from equation (15) that if the calibrated parameters α1 and β1, or calibration coefficients ceNB,n and cUE,m, are known, the downlink channel matrix HDL can be estimated from the uplink channel matrix HUL. Parameters for downlink transmission, such as a downlink transmitting precoding matrix, can thus be determined appropriately based on the uplink channel matrix.
Calibration coefficients ceNB,n and cUE,m can be calculated from downlink channel information measured in the user equipment 100 and uplink channel information measured in the radio base station 10. However, this calculation method cannot be performed when there is no user equipment 100 in a cell area of the radio base station 10. Furthermore, it will be a waste of time resources, and processing loads on the user equipment 100 will be great, if the user equipment 100 is to receive downlink pilot signals dedicated for calculating calibration coefficients and to report the calculation results to the radio base station 10. The processing loads on the user equipment 100 will also be great if the user equipment 100 is to transmit uplink pilot signals dedicated for calculating calibration coefficients.
Recently, a transmission scheme of Massive MIMO is being studied (e.g., Patent Document 1 and Non-Patent Document 3). In Massive MIMO, it is possible to perform advanced beamforming that uses a large number (e.g., 100 or more) of transmission antenna elements (e.g., 100 or more elements). Beamforming is a technique for adjusting the phase and amplitude of electric signals by weighting (applying weighting coefficients to) the electric signals supplied to transmission antenna elements in order to control the directions and shapes of radio wave beams emitted from the transmission antenna elements. Beamforming involves precoding. Massive MIMO is mainly used in radio base stations.
In Massive MIMO, a large number of transmission antenna elements are used, and consequently it takes time and effort to calibrate antennas. It can be thought that when the calibration coefficients ceNB,n and cUE,m are calculated from downlink channel information measured in the user equipment 100 and uplink channel information measured in the radio base station 10, the stated processing loads on user equipment 100 will be great and the amount of downlink channel information reported from the user equipment 100 will be massive.
In view of such circumstances, it is conceivable that a radio base station will perform self-calibration, which is antenna calibration performed locally in the radio base station. Self-calibration utilizes channel reciprocity among antenna elements of a radio base station. In self-calibration, some of the transceiving antenna elements of a radio base station receive pilot signals (pilot signals dedicated for self-calibration) that have been transmitted from other transceiving antenna elements of the radio base station, and the radio base station calculates calibration coefficients from channel state information. Therefore, there will be no processing loads on the user equipment to calculate the calibration coefficients, and a traffic will be unnecessary for reporting downlink channel state information for calculating the calibration coefficients. Furthermore, it is possible to calculate calibration coefficients even when there is no user equipment 100 in the cell area of the radio base station 10.
In self-calibration, a calibration coefficient ceNB,n is determined so as to satisfy equation (8). As described above, equation (8) can be rewritten as equation (12). Accordingly, the relationship between the uplink channel matrix and the downlink channel matrix can be expressed by the following equation (16).
                                                                        H                DL                            =                            ⁢                                                [                                                                                                              β                          1                                                                                                                                                                                                                                                                                                                                        0                                                                                                                                                                                                                                                            β                          2                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ⋱                                                                                                                                                                                                                                  0                                                                                                                                                                                                                                                                                                                                          β                          M                                                                                                      ]                                ⁢                                                      H                    UL                                    ⁡                                      [                                                                                                                        α                            1                                                                                                                                                                                                                                                                                                                                                                    0                                                                                                                                                                                                                                                                                  α                            2                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                ⋱                                                                                                                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                        β                            M                                                                                                                ]                                                  ⁢                                  H                  UL                                                                                        (        16        )            
It can be understood from equation (16) that, when calibrated parameters α1 and β1 to βM are known or a calibration coefficient ceNB,n and calibrated parameters β1 to βM are known, the downlink channel matrix HDL can be estimated from the uplink channel matrix HUL. Consequently, parameters for downlink transmission, such as a downlink transmitting precoding matrix, can be appropriately determined based on the uplink channel matrix.
A method of self-calibration will be described in detail with reference to FIGS. 2 and 3. First, the radio base station 10 transmits pilot signals from a single reference antenna element (Step S1). The reference antenna element may be any one of the transceiving antenna elements 111 to 11N. For example, the reference antenna element may be transceiving antenna element 111. During the time period in which the reference antenna element transmits pilot signals, the radio base station 10 directs other antenna elements not to transmit pilot signals.
The radio base station 10 performs channel estimation based on pilot signals that have been transmitted from the reference antenna element and are then received by calibration target antenna elements (all of the transceiving antenna elements 111 to 11N except for the reference antenna element; for example, transceiving antenna elements 112 to 11N) (Step S2). When the reference antenna element is the transceiving antenna element 111, the radio base station 10 estimates, specifically, effective channel coefficients h1,2 to h1,N in Step S2. The first argument in the subscript indicates a number for the antenna element that has transmitted a pilot signal, and the last argument in the subscript indicates a number for the antenna element that has received the pilot signal.
Next, the radio base station 10 transmits pilot signals from one of the calibration target antenna elements (Step S3). Here, the calibration target antenna element that transmits pilot signals may be any one of the calibration target antenna elements. During the time period in which this calibration target antenna element transmits pilot signals, the radio base station 10 directs other antenna elements not to transmit pilot signals.
The radio base station 10 performs channel estimation based on the pilot signals transmitted from this calibration target antenna element and then received by the reference antenna element (Step S4). When the reference antenna element is the transceiving antenna element 111, the radio base station 10 estimates, specifically, an effective channel coefficient hn,1 in Step S4. The first argument in the subscript indicates a number for the antenna element that has transmitted a pilot signal, and the last argument in the subscript indicates a number for the antenna element that has received the pilot signal.
The radio base station 10 determines whether there is any calibration target antenna element that has not transmitted pilot signals (Step S5). When the determination result is positive, Steps S3 and S4 are carried out. When all calibration target antenna elements have transmitted pilot signals, the radio base station 10 calculates calibration coefficients from the estimated effective channel coefficients (Step S6).
The effective channel coefficient hm,n from an antenna element 11m to an antenna element 11n can be expressed by the following equation (17).hm,n=TeNB,m▪gm,n▪ReNB,n  (17)
The effective channel coefficient hn,m from an antenna element 11n to an antenna element 11m can be expressed by the following equation (18).hn,m=TeNB,n▪gn,m▪ReNB,m  (18)
Here, a downlink channel gain gm,n on the air from an antenna element 11m to an antenna element 11n is equal to a downlink channel gain gn,m on the air from an antenna element 11n to an antenna element 11m. Accordingly, from equations (17) and (18), the relationship between the effective channel coefficients hm,n and hn,m can be expressed by the following equation (19).
                                                        h                              m                ,                n                                                    h                              n                ,                m                                              =                                                    T                                  eNB                  ,                  m                                            ·                              R                                  eNB                  ,                  n                                                                                    T                                  eNB                  ,                  n                                            ·                              R                                  eNB                  ,                  m                                                                    ⁢                                                      (        19        )            
In self-calibration, calibration coefficients ceNB,n are determined so as to satisfy equation (8). The calibration coefficient of the reference antenna element is configured to 1. For example, when the antenna element 111 is a reference antenna element, ceNB,1=1. In this case, from equation (8), the calibration coefficient ceNB,n can be expressed by the following equation (20).
                                          c                          eNB              ,              n                                =                                                    T                                  eNB                  ,                  1                                            ·                              R                                  eNB                  ,                  n                                                                                    R                                  eNB                  ,                  1                                            ·                              T                                  eNB                  ,                  n                                                                    ⁢                                                      (        20        )            
From equations (19) and (20), the calibration coefficient ceNB,n can be expressed by the following equation (21).
                                          c                          eNB              ,              n                                =                                    h                              1                ,                n                                                    h                              n                ,                1                                                    ⁢                                                      (        21        )            
Therefore, in Step S6, the radio base station 10 calculates, for antenna elements 112 to 11N other than the reference antenna element 111, calibration coefficients ceNB,2 to ceNB,N based on the effective channel coefficients (e.g., h1,2 to h1,N) estimated in Step S2 and the effective channel coefficients (e.g., h2,1 to hN,1) estimated in Step S4.
As can be understood from the above description, in self-calibration, during the time period in which one calibration target antenna element transmits a pilot signal, the radio base station 10 directs other antenna elements not to transmit pilot signals. Consequently, N number of periods is required. Here, N is the number of transceiving antenna elements 111 to 11N.